In a letter sent on Monday, Yoon told Xi he looks forward to communication and cooperation to improve relations between South Korea and China, South Korea's presidential office said in a statement.
Yoon has sought to reassure Beijing that his efforts to strengthen his country's alliance with the United States is not aimed at China, which is South Korea's largest trading partner.
Xi secured an unprecedented third term as leader on Sunday and introduced a new top governing body stacked with loyalists, cementing his place as the country's most powerful ruler since Mao Zedong.
North Korea's Kim Jong Un also sent a congratulatory letter to Xi on his reelection as China's leader, saying he hoped to further develop their ties, state news agency KCNA reported on Sunday.
China, which has a mutual defence treaty with North Korea and provides most of its foreign trade, has called on all sides to take steps to reduce tensions amid a record number of missile tests by the North and stepped up military drills by South Korea and the United States.
(Reporting by Josh Smith; Editing by Andrew Heavens and Mike Harrison)
